An important function of human kidneys is the excretion from the blood of urine-bound substances and adjustment of water and electrolyte elimination. Hemodialysis is a treatment method designed to compensate for renal dysfunction in elimination of urine-bound products and adjustment of the electrolyte concentration in the blood.
During hemodialysis blood is directed to an extracorporeal circulation through the blood chamber of a dialyzer; the blood chamber is separated from a dialysate chamber by a semipermeable membrane. The dialysate chamber is fed with dialysate containing blood electrolytes in a specified concentration. The concentration of the dialysate (cd) corresponds to the blood concentration of a healthy person. During a treatment, the patient's blood and the dialysate are passed by both sides of the membrane, usually in countercurrent, at a predetermined flow rate (Qb or Qd). The urine-bound products diffuse through the membrane from the blood chamber to the dialysate chamber, while at the same time the electrolytes present in the blood and in the dialysate diffused from the chamber of higher concentration to the chamber of lower concentration. The metabolism can also be influenced by applying transmembrane pressure.
To be able to optimize the blood treatment method, hemodialysis parameters must be determined during the extracorporeal blood procedure (in vivo). One parameter of particular interest is the value for the efficiency exchange of the dialyzer, represented by the so-called "clearance" or "dialysance D."
Clearance for a specified substance K denotes the virtual (calculated) blood volume from which a specified substance is removed completely in the dialyzer per minute under defined conditions. Dialysance is another term for determining the efficiency of a dialyzer, which takes into account the concentration of the eliminated substance in the dialysate. In addition to these dialyzer performance parameters, other parameters are also important, such as the values of the aqueous portion of the blood, the blood volume and the concentration in the blood at the inlet, etc.
It is relatively complex to quantify blood purification methods mathematically on the basis of measurement technology and to determine the above-mentioned dialysis parameters. A basic measurement reference work in this regard is Sargent J. A., Gotch F. A.: Principles and Biophysics of Dialysis, in: W. Drukker, F. M. Parsons, J. F. Maher (eds.) Replacement of Renal Function by Dialysis, Nijhoff, The Hague 1983.
Dialysance or clearance for a given electrolyte, e.g., sodium, at the zero ultrafiltration rate is determined as follows. The dialysance D is equal to the ratio between the mass transport for this electrolyte on the blood side (Qb.times.(cbi-cbo)) and the difference in concentration of this electrolyte between the blood and the dialysate at the inlet of the dialyzer (cbi-cdi). ##EQU1##
On the basis of mass balance: EQU Qb.multidot.(cbi-cbo)=-Qd.multidot.(cdi-cdo) (2)
It follows from equations (1) and (2) above that: ##EQU2##
where in (1) through (3):
Qb=effective blood flow PA0 Qd=dialysate flow PA0 cb=concentration of the substance in the blood PA0 cd=concentration of the substance in the dialysate PA0 i=dialyzer inlet PA0 o=dialyzer outlet
The effective blood flow is the flow of the blood portion in which the substances to be removed are dissolved, i.e., it is based on the (aqueous) solution volume for this substance. Depending on the substance, this may be the plasma water flow or the blood water flow, i.e., the total amount of water in whole blood.
The known methods of in-vivo determination of hemodialysis parameters are based on the above considerations. In this connection, an attempt is made to manage without a procedure of direct measurement of the blood side because this could represent a source of considerable risk. Therefore, the values that are to be determined must be derived solely from measurements on the dialysate side.
German Patent DE 39 38 662 C2 (European Patent EP 0 428 927 A1) describes a method of in-vivo determination of hemodialysis parameters by which the dialysate electrolyte transfer is measured at two different dialysate concentrations at the inlet. On the assumption that the concentration in the blood at the inlet is constant, dialysance can be determined according to the known method by determining the value of the differences in dialysate ion concentration at the inlet and outlet sides of the dialyzer at the time points of the first and second measurements, then by dividing this value by the difference in dialysate ion concentration at the inlet side at the times of the first and the second measurements and then multiplying by the dialysate flow. With this procedure, the relatively long measurement time proves to be a disadvantage, due to the fact that after the dialysate is adjusted to the new inlet concentration a stable steady-state condition must first be established at the dialyzer outlet before the new measurement value can be taken up. Depending on the system, it takes a certain time for a conductivity jump at the dialyzer inlet to lead to stable conditions at the dialyzer outlet.
In the article by Niels A. Lassen, Ole Henriksen, Per Sejrsen in the Handbook of Physiology, The Cardiovascular System, Vol. 3, "Peripheral Circulation and Organ Blood Flow," Part I, American Physiological Society, 1983, the response of an intracorporeal circulation to a bolus injection and subsequent measurement of the concentration is discussed in greater detail, whereby questions of signal convolution play an important part.